A merchant mixes two types of tea leaves (Darjeeling and Assam). How much amount of Darjeeling tea costing Rs. 350 per kg must be mixed with 25 kg of Assam tea of costing Rs. 480 per kg. So that on selling the mixture at Rs. 450 per kg, there is a gain of 12 1/2 % ?

Step 1: Find the Cost Price (CP) of the mixture. Given Selling Price (SP) = Rs. 450 and Profit % = 12 1/2 % = 25/2 % = 1/8 in fraction form. CP of mixture = SP / (1 + Profit fraction) = 450 / (1 + 1/8) = 450 / (9/8) = (450 * 8) / 9 = Rs. 400 per kg. Step 2: Use the Rule of Alligation to find the ratio of the two types of tea. Cost of Darjeeling Tea (Cheaper) = Rs. 350 Cost of Assam Tea (Dearer) = Rs. 480 Mean Cost Price = Rs. 400 Ratio (Quantity of Darjeeling : Quantity of Assam) = (Dearer Cost - Mean CP) : (Mean CP - Cheaper Cost) Ratio = (480 - 400) : (400 - 350) Ratio = 80 : 50 = 8 : 5 Step 3: Calculate the required quantity of Darjeeling tea. Given Quantity of Assam tea = 25 kg (which corresponds to 5 parts in our ratio). If 5 parts = 25 kg, then 1 part = 5 kg. Quantity of Darjeeling tea (8 parts) = 8 * 5 = 40 kg.